Manchester City won 2-0 at United to reach the Carabao Cup final.
Solskjaer said, "We played against a very good Manchester City team. They played well. When they play well you have to play very well to beat them. We were just lacking that little bit.
"We're getting closer. This is a much better version of United than a year ago in those semis.
"It's not psychological [losing four semis]. Sometimes you meet good teams in the semis and we just didn't have enough. We met, at the moment, probably the best team in England and we didn't have enough today.
"We want to go to a final and that would give us an extra boost. Then you got to dust this off and then we got FA Cup and big league games. Then suddenly Europa League is here again."